idris-0.9.19.1: Functional Programming Language with Dependent Types

Safe HaskellNone
LanguageHaskell98

Idris.Core.TT

Description

TT is the core language of Idris. The language has:

  • Full dependent types
  • A hierarchy of universes, with cumulativity: Type : Type1, Type1 : Type2, ...
  • Pattern matching letrec binding
  • (primitive types defined externally)

Some technical stuff:

  • Typechecker is kept as simple as possible - no unification, just a checker for incomplete terms.
  • We have a simple collection of tactics which we use to elaborate source programs with implicit syntax into fully explicit terms.

Synopsis

Documentation

data AppStatus n Source

Constructors

Complete 
MaybeHoles 
Holes [n] 

Instances

Functor AppStatus 
Eq n => Eq (AppStatus n) 
Data n => Data (AppStatus n) 
Ord n => Ord (AppStatus n) 
Show n => Show (AppStatus n) 
Typeable (* -> *) AppStatus 

data ArithTy Source

Constructors

ATInt IntTy 
ATFloat 

Instances

data Binder b Source

All binding forms are represented in a uniform fashion. This type only represents the types of bindings (and their values, if any); the attached identifiers are part of the Bind constructor for the TT type.

Constructors

Lam 

Fields

binderTy :: !b

type annotation for bound variable

Pi

A binding that occurs in a function type expression, e.g. (x:Int) -> ... The binderImpl flag says whether it was a scoped implicit (i.e. forall bound) in the high level Idris, but otherwise has no relevance in TT.

Fields

binderImpl :: Maybe ImplicitInfo
 
binderTy :: !b

type annotation for bound variable

binderKind :: !b
 
Let

A binding that occurs in a let expression

Fields

binderTy :: !b

type annotation for bound variable

binderVal :: b

value for bound variable

NLet 

Fields

binderTy :: !b

type annotation for bound variable

binderVal :: b

value for bound variable

Hole 

Fields

binderTy :: !b

type annotation for bound variable

GHole 

Fields

envlen :: Int
 
localnames :: [Name]
 
binderTy :: !b

type annotation for bound variable

Guess 

Fields

binderTy :: !b

type annotation for bound variable

binderVal :: b

value for bound variable

PVar

A pattern variable

Fields

binderTy :: !b

type annotation for bound variable

PVTy 

Fields

binderTy :: !b

type annotation for bound variable

Instances

Functor Binder 
Foldable Binder 
Traversable Binder 
Eq b => Eq (Binder b) 
Data b => Data (Binder b) 
Ord b => Ord (Binder b) 
Show b => Show (Binder b) 
Binary b => Binary (Binder b) 
NFData b => NFData (Binder b) 
Typeable (* -> *) Binder 

data Const Source

Constructors

I Int 
BI Integer 
Fl Double 
Ch Char 
Str String 
B8 Word8 
B16 Word16 
B32 Word32 
B64 Word64 
AType ArithTy 
StrType 
WorldType 
TheWorld 
VoidType 
Forgot 

Instances

type Ctxt a = Map Name (Map Name a) Source

Contexts allow us to map names to things. A root name maps to a collection of things in different namespaces with that name.

data ConstraintFC Source

Constructors

ConstraintFC 

Fields

uconstraint :: UConstraint
 
ufc :: FC
 

Instances

data DataOpt Source

Data declaration options

Constructors

Codata

Set if the the data-type is coinductive

DefaultEliminator

Set if an eliminator should be generated for data type

DefaultCaseFun

Set if a case function should be generated for data type

DataErrRev 

Instances

type DataOpts = [DataOpt] Source

data Datatype n Source

Constructors

Data 

Fields

d_typename :: n
 
d_typetag :: Int
 
d_type :: TT n
 
d_unique :: Bool
 
d_cons :: [(n, TT n)]
 

Instances

Functor Datatype 
Eq n => Eq (Datatype n) 
(Eq n, Show n) => Show (Datatype n) 

type Env = EnvTT Name Source

type EnvTT n = [(n, Binder (TT n))] Source

type Err = Err' Term Source

data Err' t Source

Idris errors. Used as exceptions in the compiler, but reported to users if they reach the top level.

Constructors

Msg String 
InternalMsg String 
CantUnify Bool (t, Maybe Provenance) (t, Maybe Provenance) (Err' t) [(Name, t)] Int 
InfiniteUnify Name t [(Name, t)] 
CantConvert t t [(Name, t)] 
CantSolveGoal t [(Name, t)] 
UnifyScope Name Name t [(Name, t)] 
CantInferType String 
NonFunctionType t t 
NotEquality t t 
TooManyArguments Name 
CantIntroduce t 
NoSuchVariable Name 
WithFnType t 
NoTypeDecl Name 
NotInjective t t t 
CantResolve Bool t 
InvalidTCArg Name t 
CantResolveAlts [Name] 
NoValidAlts [Name] 
IncompleteTerm t 
NoEliminator String t 
UniverseError FC UExp (Int, Int) (Int, Int) [ConstraintFC]

Location, bad universe, old domain, new domain, suspects

UniqueError Universe Name 
UniqueKindError Universe Name 
ProgramLineComment 
Inaccessible Name 
UnknownImplicit Name Name 
CantMatch t 
NonCollapsiblePostulate Name 
AlreadyDefined Name 
ProofSearchFail (Err' t) 
NoRewriting t 
At FC (Err' t) 
Elaborating String Name (Err' t) 
ElaboratingArg Name Name [(Name, Name)] (Err' t) 
ProviderError String 
LoadingFailed String (Err' t) 
ReflectionError [[ErrorReportPart]] (Err' t) 
ReflectionFailed String (Err' t) 
ElabScriptDebug [ErrorReportPart] t [(Name, t, [(Name, Binder t)])]

User-specified message, proof term, goals with context (first goal is focused)

ElabScriptStuck t 
RunningElabScript (Err' t)

The error occurred during a top-level elaboration script

Instances

Functor Err' 
Show Err 
NFData Err 
Eq t => Eq (Err' t) 
Data t => Data (Err' t) 
Binary a => Binary (Err' a) 
MonadException m => MonadException (ExceptT Err m) 
Typeable (* -> *) Err' 

data ErrorReportPart Source

Used for error reflection

Constructors

TextPart String 
NamePart Name 
TermPart Term 
RawPart Raw 
SubReport [ErrorReportPart] 

Instances

data FC Source

Source location. These are typically produced by the parser getFC

Constructors

FC 

Fields

_fc_fname :: String

Filename

_fc_start :: (Int, Int)

Line and column numbers for the start of the location span

_fc_end :: (Int, Int)

Line and column numbers for the end of the location span

NoFC

Locations for machine-generated terms

FileFC

Locations with file only

Fields

_fc_fname :: String

Filename

Instances

Eq FC

Ignore source location equality (so deriving classes do not compare FCs)

Data FC 
Ord FC 
Show FC 
Binary FC 
NFData FC 
SExpable FC 
Typeable * FC 

newtype FC' Source

FC with equality

Constructors

FC' 

Fields

unwrapFC :: FC
 

Instances

Eq FC' 

data ImplicitInfo Source

Constructors

Impl 

Fields

tcinstance :: Bool
 

Instances

data IntTy Source

Constructors

ITFixed NativeTy 
ITNative 
ITBig 
ITChar 

Instances

data Name Source

Names are hierarchies of strings, describing scope (so no danger of duplicate names, but need to be careful on lookup).

Constructors

UN !Text

User-provided name

NS !Name [Text]

Root, namespaces

MN !Int !Text

Machine chosen names

NErased

Name of something which is never used in scope

SN !SpecialName

Decorated function names

SymRef Int

Reference to IBC file symbol table (used during serialisation)

Instances

data NameOutput Source

Output annotation for pretty-printed name - decides colour

Constructors

TypeOutput 
FunOutput 
DataOutput 
MetavarOutput 
PostulateOutput 

Instances

data NameType Source

Constructors

Bound 
Ref 
DCon

Data constructor

Fields

nt_tag :: Int
 
nt_arity :: Int
 
nt_unique :: Bool
 
TCon

Type constructor

Fields

nt_tag :: Int
 
nt_arity :: Int
 

Instances

data NativeTy Source

Constructors

IT8 
IT16 
IT32 
IT64 

Instances

data OutputAnnotation Source

Output annotations for pretty-printing

Constructors

AnnName Name (Maybe NameOutput) (Maybe String) (Maybe String)

^ The name, classification, docs overview, and pretty-printed type

AnnBoundName Name Bool

^ The name and whether it is implicit

AnnConst Const 
AnnData String String

type, doc overview

AnnType String String

name, doc overview

AnnKeyword 
AnnFC FC 
AnnTextFmt TextFormatting 
AnnLink String

A link to this URL

AnnTerm [(Name, Bool)] (TT Name)

pprint bound vars, original term

AnnSearchResult Ordering

more general, isomorphic, or more specific

AnnErr Err 
AnnNamespace [Text] (Maybe FilePath)

A namespace (e.g. on an import line or in a namespace declaration). Stored starting at the root, with the hierarchy fully resolved. If a file path is present, then the namespace represents a module imported from that file.

AnnQuasiquote 
AnnAntiquote 

Instances

data Provenance Source

Constructors

ExpectedType 
TooManyArgs Term 
InferredVal 
GivenVal 
SourceTerm Term 

Instances

data Raw Source

Constructors

Var Name 
RBind Name (Binder Raw) Raw 
RApp Raw Raw 
RType 
RUType Universe 
RForce Raw 
RConstant Const 

Instances

data SpecialName Source

Constructors

WhereN !Int !Name !Name 
WithN !Int !Name 
InstanceN !Name [Text] 
ParentN !Name !Text 
MethodN !Name 
CaseN !Name 
ElimN !Name 
InstanceCtorN !Name 
MetaN !Name !Name 

Instances

data TC a Source

Constructors

OK !a 
Error Err 

Instances

type Term = TT Name Source

class TermSize a where Source

Methods

termsize :: Name -> a -> Int Source

Instances

data TextFormatting Source

Text formatting output

Constructors

BoldText 
ItalicText 
UnderlineText 

Instances

data TT n Source

Terms in the core language. The type parameter is the type of identifiers used for bindings and explicit named references; usually we use TT Name.

Constructors

P NameType n (TT n)

named references with type (P for Parameter, motivated by McKinna and Pollack's Pure Type Systems Formalized)

V !Int

a resolved de Bruijn-indexed variable

Bind n !(Binder (TT n)) (TT n)

a binding

App (AppStatus n) !(TT n) (TT n)

function, function type, arg

Constant Const

constant

Proj (TT n) !Int

argument projection; runtime only (-1) is a special case for 'subtract one from BI'

Erased

an erased term

Impossible

special case for totality checking

TType UExp

the type of types at some level

UType Universe

Uniqueness type universe (disjoint from TType)

Instances

Functor TT 
Show Err 
Binary CaseAlt 
Binary SC 
NFData Err 
TermSize CaseAlt 
TermSize SC 
Eq n => Eq (TT n) 
Data n => Data (TT n) 
Ord n => Ord (TT n) 
(Eq n, Show n) => Show (TT n) 
Binary (TT Name) 
NFData n => NFData (TT n) 
TermSize (TT Name) 
MonadException m => MonadException (ExceptT Err m) 
Typeable (* -> *) TT 

type Type = Term Source

data TypeInfo Source

Constructors

TI 

Fields

con_names :: [Name]
 
codata :: Bool
 
data_opts :: DataOpts
 
param_pos :: [Int]
 
mutual_types :: [Name]
 

Instances

data UConstraint Source

Universe constraints

Constructors

ULT UExp UExp

Strictly less than

ULE UExp UExp

Less than or equal to

Instances

type UCs = (Int, [UConstraint]) Source

data UExp Source

Universe expressions for universe checking

Constructors

UVar Int

universe variable

UVal Int

explicit universe level

Instances

data Universe Source

Constructors

NullType 
UniqueType 
AllTypes 

Instances

addAlist :: [(Name, a)] -> Ctxt a -> Ctxt a Source

addBinder :: TT n -> TT n Source

addDef :: Name -> a -> Ctxt a -> Ctxt a Source

allTTNames :: Eq n => TT n -> [n] Source

arity :: TT n -> Int Source

Return the arity of a (normalised) type

bindAll :: [(n, Binder (TT n))] -> TT n -> TT n Source

Introduce a Bind into the given term for each element of the given list of (name, binder) pairs.

bindingOf Source

Arguments

:: Name

^ the bound name

-> Bool

^ whether the name is implicit

-> Doc OutputAnnotation 

Pretty-printer helper for the binding site of a name

bindTyArgs :: (TT n -> Binder (TT n)) -> [(n, TT n)] -> TT n -> TT n Source

Like bindAll, but the Binders are TT terms instead. The first argument is a function to map TT terms to Binders. This function might often be something like Lam, which directly constructs a Binder from a TT term.

constDocs :: Const -> String Source

Get the docstring for a Const

constIsType :: Const -> Bool Source

Determines whether the input constant represents a type

deleteDefExact :: Name -> Ctxt a -> Ctxt a Source

discard :: Monad m => m a -> m () Source

emptyContext :: Map k a Source

emptyFC :: FC Source

Empty source location

explicitNames :: TT n -> TT n Source

Replace all non-free de Bruijn references in the given term with references to the name of their binding.

fc_end :: FC -> (Int, Int) Source

Give a notion of end location associated with an FC

fc_fname :: FC -> String Source

Give a notion of filename associated with an FC

fc_start :: FC -> (Int, Int) Source

Give a notion of start location associated with an FC

fcIn :: FC -> FC -> Bool Source

Determine whether the first argument is completely contained in the second

fileFC :: String -> FC Source

Source location with file only

finalise :: Eq n => TT n -> TT n Source

Replace every non-free reference to the name of a binding in the given term with a de Bruijn index.

fmapMB :: Monad m => (a -> m b) -> Binder a -> m (Binder b) Source

forget :: TT Name -> Raw Source

Cast a TT term to a Raw value, discarding universe information and the types of named references and replacing all de Bruijn indices with the corresponding name. It is an error if there are free de Bruijn indices.

forgetEnv :: [Name] -> TT Name -> Raw Source

freeNames :: Eq n => TT n -> [n] Source

Returns all names used free in the term

getArgTys :: TT n -> [(n, TT n)] Source

Return a list of pairs of the names of the outermost Pi-bound variables in the given term, together with their types.

getRetTy :: TT n -> TT n Source

implicitable :: Name -> Bool Source

instantiate :: TT n -> TT n -> TT n Source

Replace the outermost (index 0) de Bruijn variable with the given term

intTyName :: IntTy -> String Source

isInjective :: TT n -> Bool Source

A term is injective iff it is a data constructor, type constructor, constant, the type Type, pi-binding, or an application of an injective term.

isTypeConst :: Const -> Bool Source

liftPats :: Term -> Term Source

lookupCtxt :: Name -> Ctxt a -> [a] Source

lookupCtxtExact :: Name -> Ctxt a -> Maybe a Source

lookupCtxtName :: Name -> Ctxt a -> [(Name, a)] Source

Look up a name in the context, given an optional namespace. The name (n) may itself have a (partial) namespace given.

Rules for resolution:

  • if an explicit namespace is given, return the names which match it. If none match, return all names.

    • if the name has has explicit namespace given, return the names which match it and ignore the given namespace.
    • otherwise, return all names.

mapCtxt :: (a -> b) -> Ctxt a -> Ctxt b Source

mkApp :: TT n -> [TT n] -> TT n Source

Returns a term representing the application of the first argument (a function) to every element of the second argument.

nativeTyWidth :: NativeTy -> Int Source

nextName :: Name -> Name Source

noOccurrence :: Eq n => n -> TT n -> Bool Source

Returns true if V 0 and bound name n do not occur in the term

nsroot :: Name -> Name Source

occurrences :: Eq n => n -> TT n -> Int Source

Return number of occurrences of V 0 or bound name i the term

orderPats :: Term -> Term Source

Gather up all the outer PVars and Holes in an expression and reintroduce them in a canonical order

pEraseType :: TT n -> TT n Source

pmap :: (t -> t1) -> (t, t) -> (t1, t1) Source

pprintRaw Source

Arguments

:: [Name]

Bound names, for highlighting

-> Raw

The term to pretty-print

-> Doc OutputAnnotation 

Pretty-print a raw term.

pprintTT Source

Arguments

:: [Name]

The bound names (for highlighting and de Bruijn indices)

-> TT Name

The term to be printed

-> Doc OutputAnnotation 

Pretty-print a term

prettyEnv :: Env -> Term -> Doc OutputAnnotation Source

psubst :: Eq n => n -> TT n -> TT n -> TT n Source

pToV :: Eq n => n -> TT n -> TT n Source

Replace references to the given Name-like id with references to de Bruijn index 0.

pToVs :: Eq n => [n] -> TT n -> TT n Source

Convert several names. First in the list comes out as V 0

pureTerm :: TT Name -> Bool Source

Check whether a term has any hole bindings in it - impure if so

raw_apply :: Raw -> [Raw] -> Raw Source

raw_unapply :: Raw -> (Raw, [Raw]) Source

refsIn :: TT Name -> [Name] Source

safeForget :: TT Name -> Maybe Raw Source

safeForgetEnv :: [Name] -> TT Name -> Maybe Raw Source

showCG :: Name -> String Source

showEnv :: (Eq n, Show n) => EnvTT n -> TT n -> String Source

showEnvDbg :: (Show a, Eq a) => [(a, Binder (TT a))] -> TT a -> [Char] Source

showSep :: String -> [String] -> String Source

sInstanceN :: Name -> [String] -> SpecialName Source

sMN :: Int -> String -> Name Source

sNS :: Name -> [String] -> Name Source

spanFC :: FC -> FC -> FC Source

Get the largest span containing the two FCs

str :: Text -> String Source

subst Source

Arguments

:: Eq n 
=> n

The id to replace

-> TT n

The replacement term

-> TT n

The term to replace in

-> TT n 

As instantiate, but in addition to replacing V 0, replace references to the given Name-like id.

substNames :: Eq n => [(n, TT n)] -> TT n -> TT n Source

As subst, but takes a list of (name, substitution) pairs instead of a single name and substitution

substTerm Source

Arguments

:: Eq n 
=> TT n

Old term

-> TT n

New term

-> TT n

template term

-> TT n 

Replaces all terms equal (in the sense of (==)) to the old term with the new term.

substV :: TT n -> TT n -> TT n Source

As instantiate, but also decrement the indices of all de Bruijn variables remaining in the term, so that there are no more references to the variable that has been substituted.

sUN :: String -> Name Source

tcname :: Name -> Bool Source

Return True if the argument Name should be interpreted as the name of a typeclass.

termSmallerThan :: Int -> Term -> Bool Source

Hard-code a heuristic maximum term size, to prevent attempts to serialize or force infinite or just gigantic terms

tfail :: Err -> TC a Source

thead :: Text -> Char Source

tnull :: Text -> Bool Source

toAlist :: Ctxt a -> [(Name, a)] Source

traceWhen :: Bool -> String -> a -> a Source

txt :: String -> Text Source

unApply :: TT n -> (TT n, [TT n]) Source

Deconstruct an application; returns the function and a list of arguments

uniqueBinders :: [Name] -> TT Name -> TT Name Source

uniqueName :: Name -> [Name] -> Name Source

uniqueNameFrom :: [Name] -> [Name] -> Name Source

uniqueNameSet :: Name -> Set Name -> Name Source

unList :: Term -> Maybe [Term] Source

updateDef :: Name -> (a -> a) -> Ctxt a -> Ctxt a Source

vToP :: TT n -> TT n Source

Replace de Bruijn indices in the given term with explicit references to the names of the bindings they refer to. It is an error if the given term contains free de Bruijn indices.

weakenTm :: Int -> TT n -> TT n Source

Weaken a term by adding i to each de Bruijn index (i.e. lift it over i bindings)